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--- simulating_a_time-varying_inductor_in_spice [2024/09/09 07:23] – bm
+++ simulating_a_time-varying_inductor_in_spice [2024/09/10 09:01] (current) – bm
@@ Line 11: / Line 11: @@
 Rearranging this equation gives an expression for the current through the inductor:
-$$ i_L(t)=\frac{1}{L(t)}[L(0)i_L(0)+\int_0^t v_L(t) dt $$
+$$ i_L(t)=\frac{1}{L(t)}[L(0)i_L(0)+\int_0^t v_L(t) dt] $$
 valid if $L(t)\neq 0$ at //any// time.
+We will use this expression to simulate a time-varying inductance in LT Spice. Notice the limitation that $L(t)\neq 0$ at //any// time.
+Suppose we want we simulate a sinusoidal value in function of time with a certain offset: $L(t)$= 5 mH + 3 mH.sin(2π.100 kHz.t). In order to realize this, we have to introduce a custom component in SPICE with the following subcircuit:
+<code>
+.subckt inductor + - params: IL0=0
+.func L(time) {5m+3m*sin(2*pi*100k*time)}
+gcurr + - value={(sdt(V(+,-))+IL0*L(0))/L(time)}
+.ends
+</code>
+The current through the inductor (see equation above) is modeled via a G-type current source ''gcurr''. The integral is realized via the ''sdt'' function in SPICE. The initial value at time t=0 of the inductor must be given as parameter.
+First, we save the code for this subcircuit into a .txt-file and, for example, place this file in the same folder as your SPICE circuit file.
+Next, open the text file in LT Spice, right click on the first word ".subckt", and select "Create symbol".
+The program asks you if you wish to automatically create a symbol. Click "yes". A .asy file is created which contains your custom time-varying inductor, typically in the folder 'C:Users\YourUserName\AppData\Local\LTspice\lib\sym\AutoGenerated'
+To use the time-varying inductor in a circuit, click "component" (F2) and insert the custom inductor by searching "inductor" in the window.
+Plotting the value of the inductance in SPICE in function of time is not straightforward. Let us just check some individual times: we compare the value of the current through and voltage over the inductor (i) in the case of the time-varying inductor at time $t_i$ (after the transition period), and (ii) in the case of a static inductor with value $L(t_i)$.
+Case (i): We apply a high frequency source in order to create an envelope facilitating comparison between both cases.
+{{:simulating_a_time-varying_inductor_in_spice-1.png|}}
+At a certain time, e.g., t=50µs, the value of the inductor equals $L$(50µs)= 5 mH + 3 mH.sin(2π.100 kHz.50 µs)=5 mH.
+If we then zoom in at the simulation at t=50µs, we find the peak value of voltage over and current through the inductor.
+Case (ii): We compare this value with a static inductor of 5 mH:
+{{:simulating_a_time-varying_inductor_in_spice-2.png|}}
+We find that both the current and voltage correspond to case (i).
+We do the same for a lot of other values of time, and always find a correspondence between both cases. This is not a rigid proof, but it gives us sufficient confidence that the inductor was modeled correctly in SPICE.
+----
+**References**
+  * Biolek, D., Kolka, Z., & Biolkova, V. (2007). Modeling time-varying storage components in PSpice. In Proc. Electronic Devices and Systems IMAPS CS International Conference EDS (Vol. 2007, pp. 39-44).